A methodology for empirical complexity analysis based on Newton’s polynomial interpolation

Abstract

A cost model is a function that relates how often each part of a program runs depending on its inputs. Cost models can be derived automatically via the observation of counters: instrumentation that tracks execution of program operations. This paper defines Newton Counters: counters that can be described via a polynomial ranging on a single program input variable whose value can be read in constant time. Additionally, it shows that Newton Counters are prevalent in actual codes. Motivated by this observation, the paper introduces a methodology to derive automatic cost models. Said methodology combines static code analyses with interpolation via Newton’s divided difference method. This approach is currently available as a tool, Merlin. The effectiveness of this tool is demonstrated on 949 executable C programs taken from the Jotai collection, and on genann, a neural network library.